The invention is based on an apparatus for the sterilization of packaging containers. For example, in an apparatus known from German Offenlegungsschrift 25 09 611, a mixture of hot air and hydrogen peroxide steam is blown into a chamber into which the articles to be sterilized such as jars are introduced. Peroxide condenses on the comparatively cold walls of the containers and develops its sterilizing power there. At the successive stations the condensed peroxide is rinsed off with hot air. The exhaust air, enriched with peroxide, and the hot air-peroxide mixture flowing from the chamber are guided through filters to the outside. Apart from the fact that in the known apparatus the mixture of hot air and peroxide is not free of peroxide droplets, which cannot be completely removed by rinsing after they have settled on the walls of the containers and therefore come into contact with the material with which the containers are filled, the known apparatus has the disadvantage of a large consumption of the sterilizing agent and of hot air. This results in a considerable use of energy and in undesirable irritation to the personnel in the work area, if the filters are not working correctly. For these reasons a sterilizing apparatus with low consumption of sterilizing agent and hot air is desirable.